October Diary
On China, tyranny, and unique Hong Kong.


John Derbyshire

Pretentious ad of the month. I was strap-hanging on a crowded Long Island Railroad train, with nothing much to do but think idle thoughts, when my eye was caught by an advertisement on one of the walls. (Wall? Bulkhead? I dunno what they’re called in trains.)

The ad was for a product of the Amstel breweries. “Our light bier is more bier than light . . . The bier drinker’s delight,” it proclaimed.

I’m sure it’s lovely stuff, but . . . what’s this with “bier”? I’m aware of course that bier is the German word for “beer,” but if that’s what they intend, why don’t they write it properly, in italics? And why would they use a German word anyway, when there’s a perfectly serviceable English word to cover the substance: “beer.” That the English word “bier” already has an old and respectable meaning (“a platform or stand on which a corpse or a coffin containing a corpse rests before burial”) just compounds the offense.

Webster’s Third, to be sure, gives “bier” as a variant for “beer,” but who ever used it so? Who ever saw any necessity so to use it? But then, what necessity was there to turn buying a cup of coffee into a menu-scrutinizing exercise? I guess I’m just behind the times, as usual.

Math Corner.  The solution to last month’s puzzle is here.

For this month, an easy one. You can do this in your coffee break (espresso-macchiato break, whatever) with just high school algebra, not even Algebra II. So at least I am assured by the reader who sent it in. I don’t always tackle these problems before posting them . . . 

Your $6 scientific calculator has two functions for converting between angles expressed in fractional degrees and angles expressed in degrees:minutes:seconds. For example, key in 5.3497 (this many degrees), then hit 2nd, → D.MS and this number will be converted to 5.205892, meaning that 5.3497 degrees = 5 degrees, 20 minutes, 58.92 seconds. To reverse this, hit the key → DEG. This interprets the number being displayed as D:MM:SS.SS and converts it to number of degrees. So 5.205892 is converted to 5+20/60+58.92/60², which is 5.3497 degrees. (And of course, degrees:minutes:seconds can be interpreted as hours:minutes:seconds.) This raises the question: For what number of degrees (or hours) do these functions produce the same number? That is, we want to find a fractional part ABCDEFGH where n.ABCDEFGH degrees = n degrees AB minutes EF.GH seconds.

I’ll just add a footnote to that. Our degrees-minutes-seconds (or hours-minutes-seconds) system is a mixed one. The minutes and seconds are written hexagesimally (base 60), the rest — degrees, and parts of seconds — are written decimally (base 10). This is messy. We should go either all decimal or all hexagesimal.

The all-hexagesimal system was favored by the ancient Babylonians. It continued in use through to the late Middle Ages. I note in my book Unknown Quantity that the great 13th-century mathematician Leonardo of Pisa, a.k.a. Fibonacci, recorded the solution of a certain cubic equation in hexagesimal form as 1° 22′ 7″ 42″′ 33iv 4v 40vi, which works out to a decimal value of 1.3688081078532235 . . . 

Oh, and a second footnote, nothing to do with the brainteaser problem, just something I spotted in a math magazine. The Chinese run an international math competition just for girls — female high-school students, that is. Our lasses did well!

Gold medals were awarded to both Danielle Wang, 14, from Campbell, Calif., a freshman entering Westmont High School this fall, and Victoria Xia, 15, from Vienna, Va., a sophomore at Thomas Jefferson High School for Science and Technology. A silver medal was won by Julia Huang, 15, from Saratoga, Calif., a sophomore at Lynbrook High School. Bronze medals were awarded to Rebecca Burks, 16, from Los Altos, Calif., a junior at Danaidae Learning Studio; Christina Chen, 16, from Newton, Mass., a junior at Newton North High School; Sarah Herrmann, 15, from La Jolla, Calif., a junior at La Jolla High School; Elaine Hou, 15, from Seffner, Fla., a sophomore at C. Leon King High School; and Haotian (Tiffany) Wu, 16, from Sugar Land, Texas, a junior at Clements High School.

Congratulations to all involved! You see: Girls can so do math!